Chapter 2: Motion in a Straight Line

Chapter 2: Motion in a Straight Line

1. Frame of Reference

A frame of reference is a coordinate system used to describe the position and motion of an object.

• Observer measures motion relative to a reference point
• Can be at rest or in motion

2. Motion in a Straight Line

Motion along a straight path is called rectilinear motion.

• Position changes with time
• Described using displacement, velocity, acceleration

3. Types of Motion

• Uniform Motion: Equal distances in equal time intervals
• Non-uniform Motion: Unequal distances in equal time intervals

4. Speed and Velocity

• Speed: Distance / Time (scalar)
• Velocity: Displacement / Time (vector)

Average Speed

Total distance / total time

Average Velocity

Total displacement / total time

Instantaneous Velocity

Velocity at a particular instant of time

5. Acceleration

Rate of change of velocity with time.

• Positive acceleration → speeding up
• Negative acceleration → slowing down (retardation)

6. Equations of Motion

v = u + at
s = ut + ½at²
v² = u² + 2as

• u = initial velocity
• v = final velocity
• a = acceleration
• s = displacement
• t = time

7. Graphical Representation

• Position-Time Graph: Slope = Velocity
• Velocity-Time Graph: Slope = Acceleration
• Area under v-t graph = Displacement

8. Calculus in Motion

• Velocity = derivative of displacement
• Acceleration = derivative of velocity
• Displacement = integration of velocity

v = dx/dt
a = dv/dt
s = ∫v dt

9. MCQ One-Liners

• Velocity is a vector quantity.
• Speed is a scalar quantity.
• Slope of position-time graph gives velocity.
• Slope of velocity-time graph gives acceleration.
• Area under velocity-time graph gives displacement.
• Uniform motion means constant velocity.
• Acceleration is rate of change of velocity.
• SI unit of velocity is m/s.
• SI unit of acceleration is m/s².
• Instantaneous velocity is velocity at a particular instant.
• If acceleration is zero → motion is uniform.
• Negative acceleration is called retardation.
• Displacement can be positive or negative.
• Distance is always positive.
• Uniform acceleration means constant acceleration.
• Free fall motion has acceleration g.
• Position-time graph for uniform motion is straight line.
• Velocity-time graph for uniform acceleration is straight line.
• At rest → velocity is zero.
• Change in velocity per unit time is acceleration.

10. Numerical Problems with Solutions

1. Final Velocity

u = 10 m/s, a = 2 m/s², t = 5 s

Solution:
v = u + at
= 10 + (2×5) = 20 m/s

2. Displacement

u = 5 m/s, a = 2 m/s², t = 4 s

Solution:
s = ut + ½at²
= (5×4) + ½(2×16)
= 20 + 16 = 36 m

3. Velocity from Equation

u = 0, a = 3 m/s², s = 24 m

Solution:
v² = u² + 2as
= 0 + (2×3×24)
= 144 → v = 12 m/s

4. Average Speed

Distance = 100 m, Time = 10 s

Solution:
Average Speed = 100 / 10 = 10 m/s

5. Acceleration

u = 5 m/s, v = 25 m/s, t = 10 s

Solution:
a = (v - u)/t
= (25 - 5)/10 = 2 m/s²

6. Retardation

u = 20 m/s, v = 0, t = 5 s

Solution:
a = (0 - 20)/5 = -4 m/s²

7. Distance from Graph Concept

Velocity = 10 m/s for 5 sec

Solution:
Area under v-t graph = velocity × time
= 10 × 5 = 50 m

8. Instantaneous Velocity

If x = 5t²

Solution:
v = dx/dt = 10t
At t = 2 sec → v = 20 m/s